PART IV - Rate of Dissolution of Carbon in Molten Fe-C Alloys

The vate of dissolutioz of carbon in molten Fe-C alloys urns studied by votating- cylindrical g-vaphite sairlples in a stationary crucible containing the melt. The rate of dissolltion was determdined from the change in the bnth co)npositiorz. Alccss-tvansfev coeffi'cients, calcilated with the assurlption that the inte)yacial liquid ulas saturated with carbon, were found to be in agreement with an existing Correlation fov mass transfer jroni votating cylinders. It is corzcllrded tlat, itz the wnge of- Reynolds' numbers itzvestigated (790 to 18,000), the vate of dissolutio of carborz in Fe-C alloys is controlled by tile rate of carbon difirsion from the interface. The dissolution of carbon in molten Fe-C alloys has been the subject of a number of investigations. Most of these investigations have been inconclusive because of poorly defined experimental variables. Two of the more sophisticated studies are summarized below. Dahlke and Knacke' studied the phenomenon by, in part, immersing graphite rods into 0.5 pct carbon-steel for different lengths of time. Since the experiments were conducted in air or in CO atmospheres, the melt was strongly agitated by gas evolution. It was concluded that the change in bath composition as a function of immersion time was in agreement with the assumption that the dissolution process was transport-controlled. The hydrodynamic conditions in these experiments, however, were not well-defined and gave no indication of the nature of the dissolution process at higher fluid velocities. In a recent study Shurygin and ruk investigated the dissolution of carbon in molten Fe-C, Fe-Si, Fe-P, and Fe-Ni alloys. Small graphite disks were rotated in a crucible containing molten alloys under such conditions that only the lower face of the disk was exposed to the melt. The results of this investigation indicate that, over the range of velocities (100 to 1000 rpm) and bulk liquid concentrations (0.7 to 4.5 wt pct C) considered, the dissolution of carbon in the iron alloys is limited by the diffusion of carbon from the interface to the bulk liquid (a transport mechanism). For the particular geometry used by these authors, exact analytical solutions of hydrodynamic and diffusion problems are aailable. Hence the experimental results obtained by Shurygin and Kryuk permit the evaluation of diffusion coefficients of carbon in the four systems investigated. In the present investigation a series of experiments were conducted in which the rate of dissolution of carbon in Fe-C alloys was measured under conditions which permitted wide variation of the fluid velocity and the carbon concentration of the bulk liquid. Graphite cylinders were rotated at different speeds in a stationary concentric crucible containing various molten Fe-C alloys. THEORETICAL DEVELOPMENT In general, the resistance to mass transfer from a solid interface to a turbulent liquid is assumed to reside in a laminar boundary layer adjacent to the interface. If it is also assumed that the diffusion coefficient is independent of concentration, the steady-state rate of dissolution for the case of arbitrary liquid and solid densities can be obtained from the integration of the equations of continuity. The derivation is similar to that used by Lommel and chalmers4 for the case of pl = ps. The solution, expressed in terms where N = rate of diffusion of the solute from the interface. Exact analytical solutions of the hydrodynamic equation for the boundary layer thickness are available for only a limited number of geometries. Consequently, a mass-transfer coefficient, k, is usually